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Method for finding a solution to a linear nonstationary interval ОDЕ system. / Fominyh, A. V.
в: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Том 17, № 2, 2021, стр. 148-165.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Method for finding a solution to a linear nonstationary interval ОDЕ system
AU - Fominyh, A. V.
N1 - Publisher Copyright: © St. Petersburg State University, 2021.
PY - 2021
Y1 - 2021
N2 - The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. On the basis of these conditions, the method of the steepest descent is applied to the original problem. Some numerical examples illustrate the constructed algorithm realization.
AB - The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. On the basis of these conditions, the method of the steepest descent is applied to the original problem. Some numerical examples illustrate the constructed algorithm realization.
KW - Differential inclusion
KW - Linear nonstationary interval system of ordinary differential equations
KW - Support function
KW - The steepest descent method
KW - differential inclusion
KW - support function
KW - linear nonstationary interval system of ordinary differential equations
KW - the steepest descent method
UR - http://www.scopus.com/inward/record.url?scp=85111958362&partnerID=8YFLogxK
U2 - 10.21638/11701/SPBU10.2021.205
DO - 10.21638/11701/SPBU10.2021.205
M3 - Article
AN - SCOPUS:85111958362
VL - 17
SP - 148
EP - 165
JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
SN - 1811-9905
IS - 2
ER -
ID: 84668558